Real world experiments. We compare the generalization error with and without the SP regularization to standard baseline algorithms for data-scarce learning in the real-world (Fig. REF ). Protein is a dataset which measures the fluorescence level of \(2^{13}\)  protein sequences that link two variants of the Entacmaea quadricolor proteins different at exactly 13 amino acids  [1]}. T cell is a dataset which measures the DNA repair outcome of T cells (average length of deletions) on 1521 sites on human genome after applying double-strand breaks (DSBs) using CRISPR  [2]}. Cancer is a similar dataset on 287 sites on cancer genome [2]}. In the two latter datasets, a one-hot-encoded context sequence of size 20 around the DSB is used as the input to predict the DNA repair outcome. Following the low-\(n\)  experimental setting in [4]}, we use a subset of 30 sequences drawn uniformly at random for training and validation and use the rest for testing. We repeat each experiments \(10\times \)  with independent random splits of the data and report the RMSE in predicting the phenotype. We initialize DNNs using Xavier (equal seeds). We use the default hyperparamters in scikit-learn for the baselines. Despite minimal hyperparameter tuning and no architecture search, SP allows for a competitive performance. In particular, the SP-regularized model outperforms LASSO which applies the \(L_1\)  norm penalty on the coefficients in the polynomial representation (Fig. REF  in app:theorem:5 compares SP with different regularizers).
